Geodesic
Plane symmetric solutions in $f(\mathcal{G},T)$ gravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 518-529
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We obtain several exact solutions for a plane symmetric space–time in the framework of a recently constructed $f(\mathcal{G},T)$ theory of gravity, where $f(\mathcal{G},T)$ is a generic function of the Gauss–Bonnet invariant $\mathcal{G}$ and the trace $T$ of the energy–momentum tensor. To obtain solutions, we consider a power-law $f(\mathcal{G},T)$ gravity model and analyze the obtained results graphically. Moreover, to justify the method, we reconstruct several well-known cosmological results.
Keywords: $f(\mathcal{G},T)$ gravity, plane symmetric space–time
Mots-clés : exact solution. 
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M. F. Shamir; A. Saeed. Plane symmetric solutions in $f(\mathcal{G},T)$ gravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 518-529. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a12/

[1] S. Nojiri, S. D. Odintsov, “Modified Gauss–Bonnet theory as gravitational alternative for dark energy”, Phys. Lett. B, 631:1–2 (2005), 1–6 ; S. Nojiri, S. D. Odintsov, O. G. Gorbunova, “Dark energy problem: from phantom theory to modified Gauss–Bonnet gravity”, J. Phys. A, 39:21 (2006), 6627–6633, arXiv: hep-th/0510183 | DOI | MR | DOI | MR

[2] G. Congnola, E. Elizalde, S. Nojiri, S. D. Odintsov, S. Zerbini, “Dark energy in modified Gauss–Bonnet gravity: late-time acceleration and the hierarchy problem”, Phys. Rev. D, 73:8 (2006), 084007, 16 pp., arXiv: ; “String-inspired Gauss–Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy”, Phys. Rev. D, 75:8 (2007), 086002, 17 pp., arXiv: hep-th/0601008hep-th/0611198 | DOI | DOI

[3] S. M. Carroll, A. De Felice, V. Duvvuri, D. A. Easson, M. Trodden, M. S. Turner, “Cosmology of generalized modified gravity models”, Phys. Rev. D, 71:6 (2005), 063513, 11 pp., arXiv: astro-ph/0410031 | DOI

[4] B. M. N. Carter, I. P. Neupane, “Dynamical relaxation of dark energy: a solution to early inflation, late-time acceleration and the cosmological constant problem”, Phys. Lett. B, 638:2–3 (2006), 94–99, arXiv: hep-th/0510109 | DOI

[5] S. Nojiri, S. D. Odintsov, “Modified $f(R)$ gravity consistent with realistic cosmology: from a matter dominated epoch to a dark energy universe”, Phys. Rev. D, 74:8 (2006), 086005, 13 pp., arXiv: hep-th/0608008 | DOI

[6] S. Nojiri, S. D. Odintsov, P. V. Tretyakov, “From inflation to dark energy in the non-minimal modified gravity”, Prog. Theor. Phys. Suppl., 172 (2008), 81–89, arXiv: 0710.5232 | DOI

[7] A. De Felice, S. Tsujikawa, “Solar system constraints on $f(\mathcal{G})$ gravity models”, Phys. Rev. D, 80:6 (2009), 063516, 15 pp., arXiv: 0907.1830 | DOI

[8] S. Nojiri, S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy”, eConf, C0602061 (2006), 06; Internat. J. Geom. Meth. Modern Phys., 4:1 (2007), 115–145 | DOI

[9] S. Nojiri, S. D. Odintsov, “Unified cosmic history in modified gravity: from $F(R)$ theory to Lorentz non-invariant models”, Phys. Rep., 505:2–4 (2011), 59–144, arXiv: 1011.0544 | DOI | MR

[10] V. Fayaz, H. Hossienkhani, A. Aghamohammadi, “Power-law solution for anisotropic universe in $f(G)$ gravity”, Astrophys. Space Sci., 357:2 (2015), 136 | DOI

[11] N. M. Garcia, T. Harko, F. S. N. Lobo, J. P. Mimoso, “Energy conditions in modified Gauss–Bonnet gravity”, Phys. Rev. D, 83:10 (2011), 104032, 8 pp., arXiv: 1011.4159 | DOI

[12] M. F. Shamir, “Anisotropic cosmological models in $f(G)$ gravity”, Astrophys. Space Sci., 361:4 (2016), 147, 8 pp. | DOI | MR

[13] M. F. Shamir, “Dynamics of anisotropic universe in $f(G)$ gravity”, Astrophys. Space Sci., 362:4 (2017), 67, 8 pp. | DOI | MR

[14] M. Sharif, H. I. Fatima, “Noether symmetries in $f(G)$ gravity”, ZhETF, 149:1 (2016), 121–130 | DOI | DOI

[15] S. Nojiri, S. D. Odintsov, M. Sami, “Dark energy cosmology from higher-order, string-inspired gravity, and its reconstruction”, Phys. Rev. D, 74:4 (2006), 046004, 14 pp., arXiv: ; S. Nojiri, S. D. Odintsov, “Modified gravity and its reconstruction from the universe expansion history”, J. Phys.: Conf. Ser., 66 (2007), 012005, 22 pp. hep-th/0605039 | DOI | DOI

[16] A. De Felice, T. Suyama, T. Tanaka, “Stability of Schwarzschild-like solutions in $f(R,\mathcal{G})$ gravity models”, Phys. Rev. D, 83:10 (2011), 104035, 12 pp., arXiv: 1102.1521 | DOI

[17] S. Capozziello, A. N. Makarenko, S. D. Odintsov, “Gauss–Bonnet dark energy by Lagrange multipliers”, Phys. Rev. D, 87:8 (2013), 084037, 14 pp., arXiv: 1302.0093 | DOI

[18] S. Capozziello, M. De Laurentis, S. D. Odintsov, “Noether symmetry approach in Gauss–Bonnet cosmology”, Modern Phys. Lett. A, 29:30 (2014), 1450164, 13 pp. | DOI | MR

[19] M. F. Shamir, F. Kanwal, “Noether symmetry analysis of anisotropic universe in modified gravity”, Eur. Phys. J. C, 77:5 (2017), 286, 7 pp., arXiv: 1704.06653 | DOI

[20] B. Wu, B. Ma, “Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy”, Phys. Rev. D, 92:4 (2015), 044012, 17 pp., arXiv: 1510.08552 | DOI | MR

[21] K. Atazadeh, F. Darabi, “Energy conditions in $f(R,G)$ gravity”, Gen. Rel. Grav., 46:2 (2014), 1664, 14 pp., arXiv: 1302.0466 | DOI | MR

[22] L. Sebastiani, “Finite-time singularities in modified $F(R,G)$-gravity and singularity avoidance”, Cosmology, Quantum Vacuum and Zeta Functions, Springer Proceedings in Physics, 137, eds. D. Odintsov, D. Sáez-Gómez, S. Xambó-Descamps, Springer, Berlin, 2011, 261–270, arXiv: 1008.3041 | DOI | MR

[23] M. Sharif, A. Ikram, “Energy conditions in $f(\mathcal {G},T)$ gravity”, Eur. Phys. J. C, 76:11 (2016), 640, 13 pp., arXiv: 1608.01182 | DOI

[24] M. Sharif, A. Ikram, “Stability analysis of some reconstructed cosmological models in $f(\mathcal{G},T)$ gravity”, Phys. Dark Univ., 17 (2017), 1–9, arXiv: 1612.02037 | DOI

[25] M. Sharif, A. Ikram, “Stability analysis of Einstein universe in $f(\mathcal{G},T)$ gravity”, Internat. J. Modern Phys. D, 26:8 (2017), 1750084, 15 pp., arXiv: 1704.05759 | DOI | MR

[26] M. Sharif, A. Ikram, “Energy conditions in $f(\mathcal{G},T)$ gravity”, Eur. Phys. J. C, 76:11 (2016), 640, 13 pp., arXiv: 1608.01182 | DOI

[27] M. F. Shamir, M. Ahmad, “Noether symmetry approach in $f(\mathcal{G},T)$ gravity”, Eur. Phys. J. C, 77 (2017), 55, 6 pp., arXiv: 1611.07338 | DOI

[28] M. F. Shamir, M. Ahmad, “Some exact solutions in $f(\mathcal{G},T)$ gravity via Noether symmetries”, Modern Phys. Lett. A, 32:16, 1750086, 16 pp. | DOI | MR

[29] M. F. Shamir, “Anisotropic universe in $f(\mathcal{G},T)$ gravity”, Adv. High Energy Phys., 2017 (2017), 6378904, 10 pp. | DOI | MR

[30] M. Sharif, A. Ikram, Thermodynamics in $f(\mathcal{G},T)$ gravity, Adv. High Energy Phys., 2018, 2018, 11 pp. | DOI | MR

[31] Z. Bhatti, M. Sharif, Z. Yousaf, M. Ilyas, “Role of $f(\mathcal{G},T)$ gravity on the evolution of relativistic stars”, Internat. J. Modern Phys. D, 27:4 (2018), 1850044, 15 pp. | DOI | MR

[32] M. Sharif, M. F. Shamir, “Plane symmetric solutions in $f(R)$ gravity”, Modern Phys. Lett. A, 25:15 (2010), 1281–1288, arXiv: 0912.1393 | DOI | MR

[33] M. F. Shamir, “Plane Symmetric solutions in $f(R,T)$ gravity”, Commun. Theor. Phys., 65:3 (2016), 301–307 | DOI | MR

[34] R. Kantowski, R. K. Sachs, “Some spatially homogeneous anisotropic relativistic cosmological models”, J. Math. Phys., 7 (1966), 443–446 | DOI | MR

[35] W. Xing-Xiang, “Bianchi type-III string cosmological model with bulk viscosity in general relativity”, Chinese Phys. Lett., 22:1 (2005), 29–32 | DOI

[36] K. S. Thorne, “Primordial element formation, primordial magnetic fields, and the isotropy of the universe”, Astrophys. J., 148:1 (1967), 51–67 | DOI

[37] C. B. Collins, S. W. Hawking, “Why is the universe isotropic?”, Astrophys. J., 180 (1973), 317–334 | DOI | MR

[38] S. R. Roy, S. K. Banerjee, “Bianchi type II string cosmological models in general relativity”, Class. Quantum Grav., 12:8 (1995), 1943–1948 | DOI

[39] R. Bali, P. Kumawat, “Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity”, Phys. Lett. B, 665:5 (2008), 332–337 | DOI | MR

[40] M. Sharif, M. Zubair, “Dynamics of Bianchi $I$ universe with magnetized anisotropic dark energy”, Astrophys. Space Sci., 330:2 (2010), 399–405 | DOI

[41] G. Cognola, M. Gastaldi, S. Zerbini, “On the stability of a class of modified gravitational models”, Internat. J. Theor. Phys., 47:4 (2008), 898–910 | DOI | MR

[42] A. De Felice, S. Tsujikawa, “Construction of cosmologically viable $f(\mathcal{G})$ gravity models”, Phys. Lett. B, 675:1 (2009), 1–8, arXiv: 0810.5712 | DOI

[43] S. Tsujikawa, “Modified gravity models of dark energy”, Lectures on Cosmology, Lecture Notes in Physics, 800, ed. G. Wolschin, Springer, Berlin, 2010, 99–145, arXiv: 1101.0191 | DOI

[44] S. Nojiri, S. D. Odintsov, S. Tsujikawa, “Properties of singularities in the (phantom) dark energy universe”, Phys. Rev. D, 71:6 (2005), 063004, 16 pp., arXiv: hep-th/0501025 | DOI

[45] H. Takeno, “On plane wave solutions of field equations in general relativity”, Tensor (N. S.), 7:34 (1957), 97–102 | MR | Zbl

[46] A. Peres, “Null electromagnetic fields in general relativity theory”, Phys. Rev., 118:4 (1960), 1105–1110 | DOI

[47] T. Nordtvedt, H. Pegels, “Electromagnetic plane wave solutions in general relativity”, Ann. Phys., 17:3 (1962), 426–435 | DOI | MR

[48] V. Gaikwad, T. M. Karade, “Plane symmetric higher-dimensional space-times”, Acta Phys. Hungar., 67:3–4 (1990), 259–262 | MR

[49] K. S. Adhav, T. M. Karade, Post Raag Reports No 279, 1994

[50] S. R. Bhoyar, A. G. Deshmukh, “Plane wave solutions of the field equations of general relativity – II”, Romanian Rep. Phys., 64:4 (2012), 933–944

[51] M. L. Bedran, M. O. Calvo, F. M. Paiva, D. Soares, “Taub's plane-symmetric vacuum spacetime reexamined”, Phys. Rev. D, 55:6 (1997), 3431–3439, arXiv: gr-qc/9608058 | DOI | MR

[52] T. Feroze, A. Qadir, M. Ziad, “Modified gravity with negative and positive powers of curvature: unification of inflation and cosmic acceleration”, Phys. Rev. D, 68:12 (2003), 123512, 10 pp. | DOI

[53] M. F. Shamir, A. Saeed, “Plane symmetric solutions in $f(\mathcal{G})$ gravity”, JETP, 125:6 (2017), 1065–1070 | DOI